Notes on zygmund functions - Akhadkulov, Habibulla; Mohd Salmi, Noorani; Saaban, Azizan; Akhatkulov, Sokhobiddin (Academic Publications, Ltd., 2017)
In this paper we study a class of continuous functions satisfying a certain Zyg-mund condition dependent on a parameter γ > 0. It shown that the modulus of continuity of such functions is O(δ(log 1/δ)1-γ) if ∈ (0, 1) and O(δ(log log 1/δ )) if γ = 1. Moreover, these functions are differentiable if γ > 1. These results extend the results in literatures [4], [5].